Which of the following is a way to INCREASE the width of a confidence interval?
A. increase the chance for error
B. increase the confidence level
C. decrease the error
D. increase the sample size
The Correct Answer and Explanation is:
Correct Answer: B. Increase the confidence level
Explanation
A confidence interval is a range of values, derived from a sample, that is likely to contain the population parameter (like a mean or proportion). It is calculated using the sample statistic, the standard error, and a value from the z-distribution or t-distribution corresponding to the chosen confidence level (e.g., 90%, 95%, 99%).
The width of a confidence interval depends on three main factors:
- Confidence level
- Sample size
- Variability in the data (standard deviation)
Increasing the confidence level (e.g., from 95% to 99%) means you want to be more certain that your interval includes the true population parameter. To achieve that higher certainty, the interval must become wider to account for more possible values. That’s why increasing the confidence level increases the width of the interval.
Let’s look at the other options:
- A. Increase the chance for error: This is not a technical term. In fact, increasing the chance for error (or decreasing the confidence level) would actually make the interval narrower, not wider.
- C. Decrease the error: This typically refers to decreasing the standard error, which makes the confidence interval narrower, not wider.
- D. Increase the sample size: A larger sample size reduces the standard error, which narrows the confidence interval because the estimate becomes more precise.
Thus, the only correct answer that directly leads to a wider confidence interval is:
B. Increase the confidence level
This adjustment trades off precision (narrowness) for certainty (confidence), which is often necessary in situations requiring higher reliability in estimates, such as medical studies or quality control in manufacturing.
